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Jun 29, 2018
06/18

by
Minwon Na

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The aim of this paper is to give a corrected bijective proof of Vershik's relations for the Kostka numbers. Our proof uses insertion and reverse insertion algorithms, as in the combinatorial proof of the Pieri rule.

Topics: Combinatorics, Mathematics

Source: http://arxiv.org/abs/1601.00385

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0.0

Jun 29, 2018
06/18

by
Na Zhang

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We establish the rate of convergence in the strong law of large numbers of discrete Fourier Transform of the identically distributed random variables with finite moment of order p, where 1

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1602.07268

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0.0

Jun 29, 2018
06/18

by
Minwon Na

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We take an elementary approach to derive a generalization of Kunth's formula using Lassalle's explicit formula. In particular, we give a formula for the Kostka numbers of a shape $\mu\vdash n$ and weight $(m,1^{n-m})$ for $m=3,\;4$.

Topics: Combinatorics, Mathematics

Source: http://arxiv.org/abs/1601.00384

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1.0

Jun 28, 2018
06/18

by
Akihiro Munemasa; Minwon Na

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We give three algorithms to construct a semistandard tableau of given shape and weight, where the weight is a composition which is not necessarily a partition. With respect to a natural partial order on the set of semistandard tableaux, we show that the set of semistandard tableaux of given shape and weight has a unique greatest element and a unique least element. Two of our algorithms give each of these elements.

Topics: Combinatorics, Mathematics

Source: http://arxiv.org/abs/1507.01339

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3.0

Jun 30, 2018
06/18

by
Na Huang; Jingjing Xue

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Let ${X_j},{Y_j}(j = 1, \cdot \cdot \cdot,n)$ be vector fields satisfying H\"{o}rmander's condition and ${\Delta_L} = \sum\limits_{j = 1}^n {(X_j^2 + Y_j^2)}$. In this paper, we establish some inequalities of Dirichlet eigenvalues for degenerate elliptic partial differential operator ${\Delta_L}$ and $\Delta_L^2$. These inequalities extend Yang's inequalities for Dirichlet eigenvalues of Laplacian to the settings here and the forms of inequalities are more general than Yang's inequalities....

Topics: Mathematics, Analysis of PDEs

Source: http://arxiv.org/abs/1405.0688

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0.0

Jun 30, 2018
06/18

by
Na Huang; Pengcheng Niu

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In this paper, we establish several inequalities of Dirichlet eigenvalues for Laplace operator $\Delta $ with any order on \emph{n}-dimensional Euclidean space. These inequalities are more general than known Yang's inequalities and contain new consequences. To obtain them, we borrow the approach of Illias and Makhoul, and use a generalized Chebyshev's inequality.

Topics: Mathematics, Analysis of PDEs

Source: http://arxiv.org/abs/1405.0690

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1.0

Jun 28, 2018
06/18

by
Na Li; Shujun Wang

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This paper investigates the linear-quadratic-Gaussian (LQG) mean-field game (MFG) for a class of stochastic delay systems. We consider a large population system in which the dynamics of each player satisfies some forward stochastic differential delay equation (SDDE). The consistency condition or Nash certainty equivalence (NCE) principle is established through an auxiliary mean-field system of anticipated forward-backward stochastic differential equation with delay (AFBSDDE). The wellposedness...

Topics: Optimization and Control, Mathematics

Source: http://arxiv.org/abs/1510.00498

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0.0

Jun 28, 2018
06/18

by
Martin Andreasson; Na Li

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High-voltage direct current (HVDC) is a commonly used technology for long-distance electric power transmission, mainly due to its low resistive losses. When connecting multiple HVDC lines into a multi-terminal HVDC (MTDC) system, several challenges arise. To ensure safe and efficient operation of MTDC systems, the voltage of all terminals need to be steered to within an operational range. In this paper we study the commonly used decentralized voltage droop controller, and show that it in...

Topics: Optimization and Control, Mathematics

Source: http://arxiv.org/abs/1512.03838

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0.0

Jun 29, 2018
06/18

by
Na Zhang; Qia Li

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The constrained $\ell_0$ regularization plays an important role in sparse reconstruction. A widely used approach for solving this problem is the penalty method, of which the least square penalty problem is a special case. However, the connections between global minimizers of the constrained $\ell_0$ problem and its penalty problem have never been studied in a systematic way. This work provides a comprehensive investigation on optimal solutions of these two problems and their connections. We...

Topics: Optimization and Control, Mathematics

Source: http://arxiv.org/abs/1610.02125

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0.0

Jun 29, 2018
06/18

by
Lijian Jiang; Na Ou

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This work presents a model reduction approach to the inverse problem in the application of subsurface flows. For the Bayesian inverse problem, the forward model needs to be repeatedly computed for a large number of samples to get a stationary chain. This requires large computational efforts. To significantly improve the computation efficiency, we use generalized multiscale finite element method and least-squares stochastic collocation method to construct a reduced computational model. To avoid...

Topics: Numerical Analysis, Mathematics

Source: http://arxiv.org/abs/1604.00138

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0.0

Jun 30, 2018
06/18

by
Yong-Chao Zhang; Na Zhang

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We employ the viscosity solution technique to analyze optimal stopping problems with regime switching. Specifically, we obtain the viscosity property of value functions, the uniqueness of viscosity solutions, the regularity of value functions and the form of optimal stopping intervals. Finally, we provide an application of the results.

Topics: Mathematics, Optimization and Control

Source: http://arxiv.org/abs/1404.3372

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Jun 28, 2018
06/18

by
Kenneth J. Dykema; Wonhee Na

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We find the principal function of the completely non-normal operator l(v_1)+l(v_1)^*+i(r(v_2)+r(v_2)^*) on a subspace of the full Fock space F(H) which arises from a bi-free central limit distribution. As an application, we find the essential spectrum of this operator.

Topics: Operator Algebras, Mathematics

Source: http://arxiv.org/abs/1510.03328

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Jun 30, 2018
06/18

by
Masoud Badiei Khuzani; Na Li

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We study a stochastic primal-dual method for constrained optimization over Riemannian manifolds with bounded sectional curvature. We prove non-asymptotic convergence to the optimal objective value. More precisely, for the class of hyperbolic manifolds, we establish a convergence rate that is related to the sectional curvature lower bound. To prove a convergence rate in terms of sectional curvature for the elliptic manifolds, we leverage Toponogov's comparison theorem. In addition, we provide...

Topics: Optimization and Control, Mathematics

Source: http://arxiv.org/abs/1703.08167

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2.0

Jun 28, 2018
06/18

by
Na-Er Wang; Kan Hu

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A hypermap is an embedding of a connected hypergraph into an orientable closed surface. A covering between hypermaps is a homomorphism between the embedded hypergraphs which extends to an orientation-preserving covering of the supporting surfaces. A covering of a hypermap onto itself is an automorphism, and a hypermap is regular if its automorphism group acts transitively on the brins. Depending on the algebraic theory of regular hypermaps and hypermap operations, the abelian regular coverings...

Topics: Group Theory, Combinatorics, Mathematics

Source: http://arxiv.org/abs/1509.00941

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4.0

Jun 28, 2018
06/18

by
Shi-Mei Ma; Hai-Na Wang

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In this paper, we count a dual set of Stirling permutations by the number of alternating runs. Properties of the generating functions, including recurrence relations, grammatical interpretations and convolution formulas are studied.

Topics: Combinatorics, Mathematics

Source: http://arxiv.org/abs/1506.08716

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0.0

Jun 28, 2018
06/18

by
Kan Hu; Roman Nedela; Na-Er Wang

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A map is a 2-cell decomposition of an orientable closed surface. A dessin is a bipartite map with a fixed colouring of vertices. A dessin is regular if its group of colour- and orientation-preserving automorphisms acts transitively on the edges, and a regular dessin is symmetric if it admits an additional external symmetry transposing the vertex colours. Regular dessins with nilpotent automorphism groups are investigated. We show that each such dessin is a parallel product of regular dessins...

Topics: Combinatorics, Mathematics

Source: http://arxiv.org/abs/1508.04523

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Jun 30, 2018
06/18

by
Zhen Lei; Qi S Zhang; Na Zhao

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In this paper, we consider the Liouville property for ancient solutions of the incompressible Navier-Stokes equations. In 2D and the 3D axially symmetric case without swirl, we prove sharp Liouville theorems for smooth ancient mild solutions: velocity fields $v$ are constants if vorticity fields satisfy certain condition and $v$ are sublinear with respect to spatial variables, and we also give counterexamples when $v$ are linear with respect to spatial variables. The condition which vorticity...

Topics: Analysis of PDEs, Mathematics

Source: http://arxiv.org/abs/1701.00868

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0.0

Jun 29, 2018
06/18

by
Guannan Qu; Na Li; Munther Dahleh

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Voltage control plays an important role in the operation of electricity distribution networks, especially when there is a large penetration of renewable energy resources. In this paper, we focus on voltage control through reactive power compensation and study how different information structures affect the control performance. In particular, we first show that using only voltage measurements to determine reactive power compensation is insufficient to maintain voltage in the acceptable range....

Topics: Optimization and Control, Mathematics

Source: http://arxiv.org/abs/1606.08101

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0.0

Jun 29, 2018
06/18

by
Qia Li; Yuesheng Xu; Na Zhang

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Multi-block separable convex problems recently received considerable attention. This class of optimization problems minimizes a separable convex objective function with linear constraints. The algorithmic challenges come from the fact that the classic alternating direction method of multipliers (ADMM) for the problem is not necessarily convergent. However, it is observed that ADMM outperforms numerically many of its variants with guaranteed theoretical convergence. The goal of this paper is to...

Topics: Optimization and Control, Mathematics

Source: http://arxiv.org/abs/1601.01852

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1.0

Jun 28, 2018
06/18

by
Yibing Chen; Song Jiang; Na Liu

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In this paper, a new scheme of arbitrary high order accuracy in both space and time is proposed to solve hyperbolic conservative laws. Based on the idea of flux vector splitting(FVS) scheme, we split all the space and time derivatives in the Taylor expansion of the numerical flux into two parts: one part with positive eigenvalues, another part with negative eigenvalues. According to a Lax-Wendroff procedure, all the time derivatives are then replaced by space derivatives. And the space...

Topics: Mathematics, Numerical Analysis

Source: http://arxiv.org/abs/1508.05500

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0.0

Jun 29, 2018
06/18

by
Sen Na; Cho-Jui Hsieh

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Minimizing sum of two functions under a linear constraint is what we called splitting problem. This convex optimization has wide applications in machine learning problems, such as Lasso, Group Lasso and Sparse logistic regression. A recent paper by Gu et al (2015) developed a Semi-Proximal-Based Strictly Contractive Peaceman-Rachford Splitting Method (SPB-SPRSM), which is an extension of Strictly Contractive Peaceman-Rachford Splitting Method (SPRSM) proposed by He et al (2014). By introducing...

Topics: Optimization and Control, Mathematics, Computation, Statistics

Source: http://arxiv.org/abs/1612.09357

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0.0

Jun 30, 2018
06/18

by
Sindri Magnusson; Carlo Fischione; Na Li

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In electricity distribution networks, the increasing penetration of renewable energy generation necessitates faster and more sophisticated voltage controls. Unfortunately, recent research shows that local voltage control fails in achieving the desired regulation, unless there is some communication between the controllers. However, the communication infrastructure for distribution systems are less reliable and less ubiquitous as compared to that for the bulk transmission system. In this paper,...

Topics: Optimization and Control, Mathematics

Source: http://arxiv.org/abs/1704.00749

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0.0

Jun 28, 2018
06/18

by
Na-Er Wang; Roman Nedela; Kan Hu

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A dessin is a 2-cell embedding of a connected bipartite graph into an orientable closed surface. An automorphism of a dessin is a permutation of the edges of the underlying graph which preserves the colouring of the vertices and extends to an orientation-preserving self-homeomorphism of the supporting surface. A dessin is regular if its automorphism group is transitive on the edges, and a regular dessin is totally symmetric if it is invariant under all dessin operations. Thus totally symmetric...

Topics: Mathematics, Geometric Topology

Source: http://arxiv.org/abs/1511.06863

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0.0

Jun 29, 2018
06/18

by
Shi-Mei Ma; Toufik Mansour; Hai-Na Wang

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In this paper we study the generating polynomials obtained by enumerating signed simsun permutations by number of the descents. Properties of the polynomials, including the recurrence relations and generating functions are studied.

Topics: Combinatorics, Mathematics

Source: http://arxiv.org/abs/1605.02618

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0.0

Jun 27, 2018
06/18

by
Jeong Han Kim; Sang June Lee; Joohan Na

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When each vertex is assigned a set, the intersection graph generated by the sets is the graph in which two distinct vertices are joined by an edge if and only if their assigned sets have a nonempty intersection. An interval graph is an intersection graph generated by intervals in the real line. A chordal graph can be considered as an intersection graph generated by subtrees of a tree. In 1999, Karo\'nski, Scheinerman and Singer-Cohen [Combin Probab Comput 8 (1999), 131--159] introduced a random...

Topics: Combinatorics, Mathematics, Probability

Source: http://arxiv.org/abs/1506.03389

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5.0

Jun 26, 2018
06/18

by
Yalchin Efendiev; Seong Lee; Guanglian Li; Jun Yao; Na Zhang

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In this paper, we develop a multiscale finite element method for solving flows in fractured media. Our approach is based on Generalized Multiscale Finite Element Method (GMsFEM), where we represent the fracture effects on a coarse grid via multiscale basis functions. These multiscale basis functions are constructed in the offline stage via local spectral problems following GMsFEM. To represent the fractures on the fine grid, we consider two approaches (1) Discrete Fracture Model (DFM) (2)...

Topics: Mathematics, Numerical Analysis

Source: http://arxiv.org/abs/1502.03828

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4.0

Jun 27, 2018
06/18

by
Quan-Lin Li; Feifei Yang; Na Li

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Supermarket models with different servers become a key in modeling resource management of stochastic networks, such as, computer networks, manufacturing systems and transportation networks. While these different servers always make analysis of such a supermarket model more interesting, difficult and challenging. This paper provides a new novel method for analyzing the supermarket model with different servers through a multi-dimensional continuous-time Markov reward processes. Firstly, the...

Topics: Computing Research Repository, Performance, Probability, Mathematics

Source: http://arxiv.org/abs/1504.08150

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0.0

Jun 29, 2018
06/18

by
Sindri Magnusson; Chinwendu Enyioha; Na Li; Carlo Fischione; Vahid Tarokh

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Distributed optimization increasingly plays a central role in economical and sustainable operation of cyber-physical systems. Nevertheless, the complete potential of the technology has not yet been fully exploited in practice due to communication limitations posed by the real-world infrastructures. This work investigates fundamental properties of distributed optimization based on gradient methods, where gradient information is communicated using limited number of bits. In particular, a general...

Topics: Optimization and Control, Mathematics

Source: http://arxiv.org/abs/1603.00316

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1.0

Jun 30, 2018
06/18

by
Young-Hoon Kiem; Seung-Hyeok Kye; Joohan Na

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In this paper, we consider a system of homogeneous algebraic equations in complex variables and their conjugates, which arise naturally from the range criterion for separability of PPT states. We examine systematically these equations to get sufficient conditions for the existence of nontrivial solutions. This gives us possible upper bounds of ranks of PPT entangled edge states and their partial transposes. We will focus on the multi-partite cases which are much more delicate than the...

Topics: Quantum Physics, Mathematics, Mathematical Physics

Source: http://arxiv.org/abs/1401.3181

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1.0

Jun 30, 2018
06/18

by
Na-Rae Kim; Andrew W. Eckford; Chan-Byoung Chae

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In this paper, we propose a symbol interval optimization algorithm in molecular communication with drift. Proper symbol intervals are important in practical communication systems since information needs to be sent as fast as possible with low error rates. There is a trade-off, however, between symbol intervals and inter-symbol interference (ISI) from Brownian motion. Thus, we find proper symbol interval values considering the ISI inside two kinds of blood vessels, and also suggest no ISI system...

Topics: Mathematics, Computing Research Repository, Information Theory

Source: http://arxiv.org/abs/1407.5776

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1.0

Jun 29, 2018
06/18

by
Quan-Lin Li; Rui-Na Fan

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To reduce automobile exhaust pollution, traffic congestion and parking difficulties, bike-sharing systems are rapidly developed in many countries and more than 500 major cities in the world over the past decade. In this paper, we discuss a large-scale bike-sharing system under Markovian environment, and propose a mean-field matrix-analytic method in the study of bike-sharing systems through combining the mean-field theory with the time-inhomogeneous queues as well as the nonlinear QBD...

Topics: Probability, Dynamical Systems, Performance, Computing Research Repository, Mathematics

Source: http://arxiv.org/abs/1610.01302

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0.0

Jun 30, 2018
06/18

by
Shih-Hao Huang; Mong-Na Lo Huang; Kerby Shedden; Weng Kee Wong

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We construct optimal designs for group testing experiments where the goal is to estimate the prevalence of a trait by using a test with uncertain sensitivity and specificity. Using optimal design theory for approximate designs, we show that the most efficient design for simultaneously estimating the prevalence, sensitivity and specificity requires three different group sizes with equal frequencies. However, if estimating prevalence as accurately as possible is the only focus, the optimal...

Topics: Statistics Theory, Statistics, Mathematics

Source: http://arxiv.org/abs/1701.00888

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1.0

Jun 30, 2018
06/18

by
Na Deng; Wuyang Zhou; Martin Haenggi

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The spatial structure of transmitters in wireless networks plays a key role in evaluating the mutual interference and hence the performance. Although the Poisson point process (PPP) has been widely used to model the spatial configuration of wireless networks, it is not suitable for networks with repulsion. The Ginibre point process (GPP) is one of the main examples of determinantal point processes that can be used to model random phenomena where repulsion is observed. Considering the accuracy,...

Topics: Networking and Internet Architecture, Mathematics, Probability, Computing Research Repository,...

Source: http://arxiv.org/abs/1401.3677

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Jun 30, 2018
06/18

by
H. Birkan Yilmaz; Na-Rae Kim; Chan-Byoung Chae

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Communication via diffusion (CvD) is an effective and energy efficient method for transmitting information in nanonetworks. In this work, we focus on a diffusion-based communication system where the reception process is an absorption via receptors. Whenever a molecule hits to the receiver it is removed from the environment. This kind of reception process is called first passage process and it is more complicated compared to diffusion process only. In 3-D environments, obtaining analytical...

Topics: Mathematics, Emerging Technologies, Computing Research Repository, Information Theory

Source: http://arxiv.org/abs/1401.3410

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1.0

Jun 29, 2018
06/18

by
Quan-Lin Li; Rui-Na Fan; Jing-Yu Ma

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During the last decade bike sharing systems have emerged as a public transport mode in urban short trips in more than 500 major cities around the world. For the mobility service mode, many challenges from its operations are not well addressed yet, for example, how to develop the bike sharing systems to be able to effectively satisfy the fluctuating demands both for bikes and for vacant lockers. To this end, it is a key to give performance analysis of the bike sharing systems. This paper first...

Topics: Optimization and Control, Probability, Performance, Computing Research Repository, Mathematics

Source: http://arxiv.org/abs/1606.04805

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1.0

Jun 29, 2018
06/18

by
Quan-Lin Li; Chang Chen; Rui-Na Fan; Liang Xu; Jing-Yu Ma

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The bike sharing systems are fast increasing as a public transport mode in urban short trips, and have been developed in many major cities around the world. A major challenge in the study of bike sharing systems is that large-scale and complex queueing networks have to be applied through multi-dimensional Markov processes, while their discussion always suffers a common difficulty: State space explosion. For this reason, this paper provides a mean-field computational method to study such a...

Topics: Probability, Dynamical Systems, Performance, Computing Research Repository, Mathematics

Source: http://arxiv.org/abs/1603.09560